It can be upsetting, and I’m not necessarily going to be keeping it to the realm of only statistics. Sometimes, you may not want to know what I know about death.

BROKENHEARTSYNDROME

Someone wrote an email to me recently, asking about mortality assumptions when pricing annuities:

For pricing a joint annuity is it normal to assume mortality of the two lives are independent? I’d guess that there might be some positive correlation (e.g. b/c of life style), but I’ve never seen any reference made to that.

Here is the answer I wrote:

For annuities, yes.

For life insurance, no.

Let me explain why — there is a correlative effect, in that if one dies, the other has a heightened mortality, at least in the short run [there really is a “broken heart” syndrome.]

Actuaries developed copulas originally for pricing Joint Last Survivor life insurance, because the results were bad (from the insurer point of view) if you used the independence assumption. The copulas had some built in positive correlation.

With the built in positive correlation, the joint life status has a shorter life expectancy. The issue with independence is that the joint life status for the same base mortality tables will give you a longer life expectancy — bad for life insurance.

You don’t want to assume the joint lives will have shorter lifespan when pricing annuities. That’s not being conservative. The independence assumption is conservative for joint annuities.

FWIW, yes, these are the copulas involved in the infamous pricing of CDOs that was involved in stuff like the Big Short. Recipe for Disaster: The Formula That Killed Wall Street from 2009 can give you some info re: that, and no, it’s not exactly the copulas that did it, but I don’t want to go down that particular rabbit hole right now.

There are lots of different copulas that can be used, and the type used for joint life insurance policies work just fine for that purpose.

Johnny Cash and June Carter met backstage at the Grand Ole Opry. It was a little like a country song: he was married, she recently divorced, and an affair ensued; both singers had young children, and Cash would have three more with his first wife before she left him in 1966, citing his drinking and carousing. Two years later, he proposed to Carter on stage and, despite having turned him down numerous times before, she accepted. They’d each found a life match.

It ended like a country song, too. In 2003, Carter died in Nashville of complications from heart surgery, and Cash followed her to the grave four months later. The heart complication for him, it seemed, was that it was broken: “It hurts so bad,” he told the audience at the last concert he would give. The pain, he said, tuning his guitar, close to tears, was “the big one. It’s the biggest.”

Cash was speaking for many a bereaved partner – and well before Johnny ever met June, scientists had noticed that cases of spouses dying in rapid succession were not at all unusual. By the 1980s, medical researchers had started writing about “stress cardiomyopathy”, or “apical ballooning syndrome”, the ungainly name for the peculiar condition whereby an individual’s brain, following an intense emotional trauma, would inexplicably release chemicals into the bloodstream that weakened the heart – in some cases, causing it quite literally to break.

The medical community was interested because it offered a chance, potentially, to intervene and prolong life. Another industry was interested in the phenomenon, too – but less to stop it and more to understand it. These were the actuaries working in life assurance. Actuarial science is the study of the statistics surrounding life and death – and the statistics surrounding the broken heart phenomenon were striking. Pages and pages of death records showed the same marked trend: that in human couples, the death of one partner significantly increases the chances of the death of the other. Dying of a broken heart – in the most general sense, not necessarily from stress cardiomyopathy – was not a rare occurrence, but something of a statistical probability. So much so that life assurers, in order to conduct their business, needed to incorporate it into their models. In a March 2008 study, Jaap Spreeuw and Xu Wang of the Cass Business School observed that in the year following a loved one’s death, women were more than twice as likely to die than normal, and men more than six times as likely. “This implies … that joint life annuities [in which payments continue at the same price until both partners die] are underpriced while last survivor annuities [in which payments increase after one partner dies] are overpriced,” concluded the authors.

Even before the definitive Cass study, however, actuaries had begun to incorporate the broken heart trend into their mathematical models calculating the chances of clients dying. How could such an ephemeral relationship be reliably captured? The actuaries, of course, relied on probability. While they could not hope to devise a model that predicted the likelihood of death from a broken heart for a specific couple, they could use statistical science to devise a fairly accurate picture across a group of people.

Actuaries noticed that joint last survivor life insurance pricing did not work too well if you assumed independence of death rates. The copulas fixed that part.

Similarly, actuaries have noticed all sorts of risk factors in pricing insurance, many times years before the medical research showed it.

There’s a reason for this.

It’s called money.

Insurance companies losemoney if life insurance policyholders die in a pattern such that they’re dying earlier than we expected them to. This happens every so often, and the actuaries start looking at the underwriting info against the claims data to try to figure out what happened.

Actuaries knew of the hideous life expectancy difference for smokers vs. nonsmokers before the Surgeon General’s report in 1964 came out.

Thing is — actuaries don’t really care why there’s a difference in risk levels. We just need to be able to capture these differences. This is coming out more with predictive analytics, and some of the risk indicators are one people really don’t want to hear about.

So I’m not going to let you know.

Right now. Maybe another time.

ANECDATA

It wasn’t just that email that made me do this post. It was also a blog post by Kim du Toit, whose wife recently died: A Reason To Live:

It seems to be a fact of life that when one spouse of an elderly couple dies, it’s not long before the other dies too. I haven’t looked up any actual stats for this — it’s purely an observation — but it seems that if it’s the wife that goes first, it doesn’t take long before the widower follows. It seems especially true if the couple is truly elderly — say, in their 70s or 80s, and I believe that spousal deaths “days after” (and sometimes even “hours after”) are almost a given once a couple has reached their 90s together.

I know exactly how they feel.

What I’ve figured out, speaking just for myself, is that once one is older, the death of a spouse takes away a large reason for the survivor to stay alive. The kids are grown, have left the house and are getting on with their own lives. (Which is exactly as it should be. Nobody should be held to their parents so tightly in adulthood that they can’t follow their own lives’ dreams and ambitions.)

It’s not just for older folks with empty nests, btw. I have anecdata there, too, but let me elide over that.

You don’t hear about broken heart syndrome as much with younger people, because the base mortality rate is already so low to begin with. You could triple or quadruple that death rate, and you’d still barely notice. There is an effect, but it’s not all that noticeable at young ages — increasing a really low number stays really low.

But you do notice it once death rates accelerates in the ages of 60+ years.

This broken heart syndrome is a relative risk issue, you see. The relative risk increases, but that doesn’t mean the mortality rate becomes 100%.

My own grandparents, both sets of which had been married for a long time, outlived their spouses by quite some time: my paternal grandmother outlived granddaddy by over 25 years, my maternal grandfather outlived nana by 8-ish years.

Just because something becomes noticeably more likely doesn’t mean it will happen.

People have their various explanations, and Kim has his own. All I can tell you is that yes, it is a real phenomenon.